Inference of the optical depth to reionization from low multipole temperature and polarization Planck data. Issue 1 (11th August 2021)

• Record Type: Journal Article
• Authors: de Belsunce, Roger; Gratton, Steven; Coulton, William; Efstathiou, George
• Is Part Of: Monthly notices of the Royal Astronomical Society. Volume 507:Issue 1(2021)
• Page Start: 1072
• Page End: 1091
• Publication Date: 2021-08-11
• Subjects: methods: data analysis -- cosmic background radiation -- cosmological parameters; Astronomy -- Periodicals; Periodicals; 520.5
• DOI: 10.1093/mnras/stab2215
• Languages: English
• ISSNs: 0035-8711

Abstract

ABSTRACT: This paper explores methods for constructing low multipole temperature and polarization likelihoods from maps of the cosmic microwave background anisotropies that have complex noise properties and partial sky coverage. We use Planck 2018 High Frequency Instrument (HFI) and updated SRoll2 temperature and polarization maps to test our methods. We present three likelihood approximations based on quadratic cross spectrum estimators: (i) a variant of the simulation-based likelihood (SimBaL ) techniques used in the Planck legacy papers to produce a low multipole EE likelihood; (ii) a semi-analytical likelihood approximation (momento ) based on the principle of maximum entropy; (iii) a density-estimation 'likelihood-free' scheme (delfi ). Approaches (ii) and (iii) can be generalized to produce low multipole joint temperature-polarization ( TTTEEE ) likelihoods. We present extensive tests of these methods on simulations with realistic correlated noise. We then analyse the Planck data and confirm the robustness of our method and likelihoods on multiple inter- and intra-frequency detector set combinations of SRoll2 maps. The three likelihood techniques give consistent results and support a low value of the optical depth to reoinization, τ, from the HFI. Our best estimate of τ comes from combining the low multipole SRoll2 momento ( TTTEEE ) likelihood with the CamSpec high multipole likelihood and is $\tau = 0.0627^{+0.0050}_{-0.0058}$ . This is consistent with the SRoll2 team's determination of τ, though slightly higher by ∼0.5σ, mainly because of our joint treatment of temperature and polarization.